In a generally disappointing game, Tunisia went ahead against the run of play in the 34th minute of the Group E match, failed to build on the lead and paid the price when Djalma snapped a rebound in the 73rd minute.
Mali and Mauritania were meeting later on Monday in the second half of a double bill at the Suez Stadium.
The game was played in hot conditions, although a sea breeze made the temperature more bearable and it did not seem to unduly affect the players. The stadium was barely one quarter full with spectators scattered around the arena.
"It was a very difficult and demanding game ... I think we played the best African team," said Angola coach Srđjan Vasiljevic. "We had enormous difficulties in the preparation period but we faced a strong rival and got a good result."
There was a lot of probing by both sides early on but Angola were more positive and Wilson Eduardo was close with a looping shot across the face of the goal.
Tunisia went ahead with a penalty as Msakni found Sliti Naim who cut inside Salomao Paizo and was brought down by the Angolan's clumsy lunge. There were few complaints from Angola and Msakni fired the spot kick into the roof of the net.
The North Africans, the second highest African team in the FIFA rankings, sat on their lead and Angola, back at the tournament after missing the previous two, took advantage.
Tunisia goalkeeper Farouk Ben Musthapha spilled a shot by Matheus and Djalma turned in the rebound.
Tunisia twice came close to a stoppage time winner as Wahbi Khazri prodded the ball wide after a free kick and Msakni sent a free shot wide of the post from the edge of the penalty area.
"We came here to show our value without any promise or fixed objectives," said Vasiljevic. "We have a plan to play good football and compete with the best African teams."
(Writing by Brian Homewood; Editing by Ken Ferris and Alison Williams)
